Apparatus and method for determining net section parameters of truss connector plates

ABSTRACT

Net section parameters of connector plates at selected truss joints are determined by representing each wood member as a corresponding two-dimensional polygon and the connector plate as a rectangle of predetermined dimensions corresponding to the actual dimensions of the plate. When the plate is positioned at a particular truss joint, the area of intersection between the plate rectangle and the polygon defines an intersection polygon. The intersection polygon is rotated and the Cartesian coordinate system of the intersection polygon is redefined so that a first axis thereof is aligned with a central major axis extending along a geometric center of a major surface of the particular wood member. The maximum and minimum coordinates of the intersection polygon along a second axis of the redefined coordinate system, which is perpendicular to the first axis thereof, are added together to determine the length of overlap of the connector plate along an axis perpendicular to the central major axis of the wood member, thereby defining the net section parameter of the corresponding wood member.

FIELD OF THE INVENTION

The present invention relates to wood trusses used in buildingconstruction and in particular to an apparatus and method fordetermining net section parameters of metal connector plates at therespective joints of the wood truss.

BACKGROUND OF THE INVENTION

A conventional truss is typically comprised of top and bottom chords, aplurality of web members extending between the top and bottom chords anda plurality of metal toothed connector plates for securing the ends ofeach web member to the top and bottom chords, thereby completing thefabrication of the truss. It is critical that these metal connectorplates be properly positioned and attached at the joints between the webmembers and chords in order to provide the necessary structural strengthand integrity.

DESCRIPTION OF THE PRIOR ART

According to prior practice, computer software programs are often usedto assist the truss designer in the selection and placement of theconnector plates. Once the truss is engineered to determine the size andshape threreof, each joint is analyzed to determine the proper sizeconnector plate to be used and the proper position of the connectorplate on the joint. Using an iterative process, different sizedconnector plates can be tested to find a proper connector plate for eachtruss joint based upon selected parameters applicable to that joint. Theplate is positioned within the outermost boundaries of the truss andselected parameters, such as the area overlap of the plate on the jointmembers and shear and tension stresses on the joint members, are testedto determine whether the particular connector plate is suitable for thatjoint.

The position of the connector plate on the joint is determined by firstplacing the geometric center of the plate coincident with thepredetermined geometric center of the joint and checking the pointcoordinates (based upon a reference Cartesian coordinate system) of eachof the four corners of the rectangular plate to determine whether any ofthe four corners of the plate is outside of the outer boundary of thejoint. The plate is then moved accordingly to position the plate withinthe outer boundary of the joint.

One problem associated with this prior art technique is that only theouter boundaries of the truss are considered and not the innerboundaries thereof. For example, in the case of trusses used in buildingattics, the connector plates may not be able to extend beyond the innerboundaries of the truss. Another problem with prior art placementtechniques is that "non-standard" joints are often modeled by "standard"joints, which are based upon an estimation of the shape of the joint andnot upon the actual shape thereof. For example, the estimated shape ofthe joint may be based upon an assumed number of cuts in the jointmembers, but the actual shape of the joint may involve a differentnumber of cuts and hence a different shape from that estimated, therebyleading to errors in the placement of the plates.

It is also difficult using prior art techniques to accurately determinearea of overlap and net section parameters of the plate on the joint notonly because the shape of the joint members is not always well-defined,but also because it is difficult to determine the positions of thecorners of the rectangular plate after the plate is superimposed on thejoint members. These parameters are usually estimated, which often leadsto significant errors.

OBJECTS OF THE INVENTION

It is, therefore, the principal object of the present invention toprovide an improved apparatus and method for determining net sectionparameters of metal connector plates in a wood truss.

Another object of the invention is to provide an apparatus and method bywhich net section parameters of the connector plates on a truss jointcan be accurately determined for truss joints of various shapes andsizes.

SUMMARY OF THE INVENTION

These and other objects are accomplished in accordance with the presentinvention wherein an apparatus and method for determining net sectionparameters of truss connector plates is provided. After a connectorplate is positioned at a particular truss joint, which represents theintersection of two or more wood members of the truss, the net sectionparameters of that particular plate are determined by measuring therespective lengths of overlap of the plate on the individual woodmembers of the joint. The respective lengths of overlap are determinedby the steps of: (1) establishing a Cartesian coordinate system, theorigin of which corresponds to a predetermined reference point on thejoint; (2) representing each wood member as a corresponding twodimensional polygon, each side of which is defined by a correspondingmember vector; (3) representing the connector plate as a rectangle ofpredetermined dimensions corresponding to the actual dimensions of theplate, each side of the rectangle being defined by a corresponding oneof a plurality of plate vectors; (4) selecting a particular one of thewood members and determining the area of intersection of the rectanglewith the polygon defined by the particular wood member, the area ofintersection defining an intersection polygon; (5) rotating theintersection polygon and redefining the Cartesian coordinate system ofthe intersection polygon so that a first axis thereof is aligned withthe central major axis extending along the approximate geometric centerof a major surface of the particular wood truss member; and (6)measuring the maximum and minimum coordinates of the intersectionpolygon along the second axis of the redefined coordinate system, whichis perpendicular to the first axis thereof, and adding the values of themaximum and minimum coordinates to determine the total length of overlapof the connector plate along an axis perpendicular to the central majoraxis of the particular wood member.

The stress acting on the particular wood member is computed by dividingthe force acting along the central major axis of the corresponding woodmember by the product of the sum of the corresponding minimum andmaximum coordinates along the second axis and the thickness of the woodmember, as measured along an axis which is perpendicular to the majorsurface of the wood member. The computed stress is compared with apredetermined maximum allowable stress to determine whether the netsection parameter for that particular wood member has been met. Steps(4), (5), and (6) set forth above are repeated for each wood member ofthe joint to determine the length of overlap of the plate along an axisperpendicular to the corresponding central axis of each wood member andthe stress acting in each wood member is computed as set forth above todetermine the net section parameter of the plate on each wood member ofthe joint.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects and advantages of the invention will be apparent from thedetailed description and claims when read in conjunction with theaccompanying drawings wherein:

FIGS. 1A and 1B are respective elevation views of first and secondembodiments of a wood truss with metal connector plates attached at therespective joints of the truss;

FIG. 2 is a sectional view of a heel joint of a truss, illustrating theestablishment of a Cartesian coordinate system for reference purposes;

FIG. 3 is a sectional view of the heel joint illustrated in FIG. 2,which shows the individual members of the truss joint being defined by aplurality of vectors rotating in a counterclockwise direction aroundeach of the members;

FIG. 4 is a flow diagram illustrating the system and method fordetermining net section parameters of a connector plate at acorresponding truss joint in accordance with the present invention;

FIGS. 5A and 5B are respective sectional views of an interior trussjoint, illustrating the determination of the area of overlap of theconnector plate on one of the members of the joint;

FIGS. 6A-6C are respective sectional views illustrating thedetermination of the net section check parameter of the connector platewith respect to one of the joint members; and

FIG. 7 is a block diagram of a computer system for executing thepreferred embodiment of the method for determining net sectionparameters of a connector plate at a corresponding truss joint inaccordance with the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In the description which follows like parts are marked throughout thespecification and drawings, respectively. The drawings are notnecessarily to scale and in some instances proportions have beenexaggerated in order more clearly depict certain features of theinvention.

Referring to FIG. 1A, a conventional roof truss 10 is depicted. Truss 10is comprised of a top chord 12, a bottom chord 14 and a plurality of webmembers 16 interconnecting top and bottom chords 12 and 14. Top chord 12is comprised of two wood members, respective first ends of whichintersect at an obtuse angle to define apex 18 of truss 10. Therespective second ends of the two wood members, opposite from therespective first ends thereof, intersect bottom chord 14 at respectiveopposite sides of truss 10 to define respective heel joints 19. Theintersections between web members 16 and top and bottom chords 12 and 14also define respective joints on truss 10. Toothed metal connectorplates 20 are disposed at predetermined positions on the correspondingtruss joints to hold the wood members in position and provide structuralintegrity for truss 10.

Referring to FIG. 1B, another embodiment of a roof truss is depicted.Truss 22 is similar to truss 10 except that bottom chord 24 is alsocomprised of a pair of wood members, respective first ends of whichintersect at an obtuse angle below apex 26 of truss 22 so that truss 22defines a vaulted structure, such as that frequently used in atticareas. The intersection of respective first ends of the two memberscomprising top chord 28 defines apex 26. Respective second ends of thewood members comprising top chord 28, opposite from the respective firstends thereof, intersect corresponding second ends of the wood memberscomprising bottom chord 24 to define respective heel joints 30 onopposite sides of trus 22. Wooden web members 32 interconnect top andbottom chords 28 and 24. One skilled in the art will recognize that webmembers 32 are oriented differently from web members 16 of truss 10, butthat their function is substantially the same. Toothed metal connectorplates 34 are disposed at predetermined positions on the truss joints tosecure the joints as previously described.

Area overlap and net section parameters for a connector plate at a trussjoint is determined according to a computer-based routine, as describedbelow with reference to FIG. 7.

Referring to FIGS. 2 and 3, a Cartesian coordinate system is establishedhaving a point of origin (0,0), indicated at 35, which corresponds to apredetermined reference point on the truss. In FIG. 2, the origin pointis at the lower left edge of the truss, which corresponds to the centerof left heel joint 36 depicted in FIG. 2. Heel joint 36 is defined bythe intersection of respective ends of diagonally oriented top chord 38and horizontal bottom chord 40. The X-axis runs horizontally along thebottom edge of bottom chord 40 and the Y-axis runs vertically along theleft side of heel joint 36. As shown in FIG. 3, top and bottom chords 38and 40 are represented by corresponding polygons, the respectiveperimeters of which are defined by respective member vectors. Asindicated by the arrows in FIG. 3, the member vectors define acounterclockwise rotation around the corresponding polygon. The jointboundaries in this example are defined by vector 42 extending along theleft side of joint 36 and vector 44 extending along the bottom edge ofjoint 36.

Referring to FIGS. 4, 5A and 5B, the area of overlap of a connectorplate on each of the wood members of a particular truss joint isdetermined and compared with the minimum area overlap acceptable forthat joint. Each of the wood members of the joint is assigned asequential number and the routine begins with the first wood member. Theperimeter of a major surface of each wood member is defined bycorresponding member vectors and the plate perimeter is defined bycorresponding plate vectors, as described previously. Once the plate isproperly positioned on the joint, the program determines whether arectangle representing the connector plate intersects the polygonrepresenting the first wood member of the joint. If no intersectionexists, there is no area of overlap between the connector plate and theparticular wood member, which necessitates the selection of a largerplate. If an intersection exists, the program determines the location ofthe area of intersection between the rectangle and the first wood memberby determining the coordinates of the points of intersection between theplate vectors and the corresponding member vectors. The area ofintersection is defined by a polygon, which represents the area overlapof the connector plate on the first wood member.

For example, in FIGS. 5A and 5B, an interior truss joint 78 is depictedin which a first web member 80 intersects bottom chord 82 diagonally,and a second web member 84 intersects bottom chord 82 substantially atright angles. The overlap of rectangle 86 on first web member 80 definesa substantially trapezoidal shaped polygon 88 with five sides and fivecorner points 1,2,3,4 and 5. The area of polygon 88 determines the areaoverlap parameter.

The area of polygon 88 is arrived at by solving the following equationknown as Green's Theorem for the area of a polygon given an ordered setof X and Y coordinates: ##EQU1## where A is the area of polygon 88, n isthe number of corner points of polygon 88 (in this example, n=5), andXi, Yi are the Cartesian coordinates of the ith corner point of polygon88. The equation involves multiplying the difference between theY-coordinates of each pair of adjacent corner points by the sum of theX-coordinates of each pair of adjacent corner points, dividing theproduct by 2, and then summing the results for all n pairs of cornerpoints. In the example illustrated by FIGS. 5A and 5B, corner point 1will also be corner point 6 so that the calculations using Green'sTheorem will proceed counterclockwise around polygon 88, beginning withcorner points 1 and 2 and ending with corner points 5 and 6 (same as 1).

The computed area of polygon 88 is compared with the predeterminedparameter representing the minimum area overlap which is acceptable forthat particular wood member of the joint. If the computed area overlapexceeds the minimum acceptable area overlap, then first web member 80 isdetermined to have sufficient area coverage by that particular connectorplate represented by rectangle 86 and the next parameter, namely netsection coverage, will be checked. If the area overlap falls short ofthe minimum acceptable area overlap, a larger plate is selected and theprocess will begin anew with respect to the new plate.

Net section coverage is illustrated by FIGS. 6A and 6B. The net sectioncoverage check involves a determination of whether the connector plateprovides sufficient overlap coverage along an axis which isperpendicular to the line of force acting along a major axis of aparticular wood member of a truss joint to prevent the plate frompulling out of the joint. This parameter is dependent upon the type oflumber being used and the design of the joint rather than upon the typeof plate being used. As depicted in FIG. 4, once the area overlapparameter has been satisfied for web member 80, the net section check isperformed for web member 80 using the same intersection polygon 88except that intersection polygon 88 is rotated to redefine the Cartesiancoordinate system thereof so that the X-axis is aligned with centralmajor axis 90 of web member 80, which extends along the approximategeometric center of a major surface of web member 80. The Y-axis of therotated coordinate system is oriented perpendicularly with respect tocentral major axis 90 of web member 80. As shown in FIG. 6C, the maximum(H1) and the minimum (H2) coordinates of intersection polygon 88 alongthe Y-axis are determined and are added together to determine the totallength of overlap of rectangle 86 on web member 80. The stress acting onweb member 80 tending to dislodge the plate from web member 80 iscomputed according to the following equation:

    S=F/(H1+H2)×Z

where S is the stress acting on the member, F is the force acting alongcentral major axis 90 in the member and Z is the thickness of themember, measured along an axis which is perpendicular to the majorsurfaces of the member.

The computed stress is then compared with the maximum allowable stressfor that member. If the computed stress is less than the maximumallowable stress, the net section parameter is satisfied. Otherwise,sufficient net section coverage is not available, and a larger platemust be selected. The area overlap and the net section coverage aredetermined for each web member of the joint. The chosen connector platemust satisfy the applicable parameters for each joint member. Otherwise,the plate is discarded in favor of a larger plate.

When all of the applicable parameters are satisfied for a particularplate, the plate information, including the identification of the plateand the position thereof on the joint, is stored in the system memory.The program then moves to the next joint in sequence, and theaforementioned procedure and checks are repeated with respect to thenext joint. When all of the truss joints have been properly plated, thetask is completed and the truss can be assembled according tospecifications.

Referring to FIG. 7, the program routine described above is preferablyimplemented in connection with a digital computer system, such as apersonal computer having a DOS-based operating system. Truss profileinformation, including the span of the truss, the truss pitch and therespective positions of the web members connecting the top and bottomtruss chords to define the respective truss joints, are entered by auser via an input device 110, such as a keyboard, into a centralprocessing unit (CPU) 112. CPU 112 loads the input data into a randomaccess memory (RAM) 114. A storage device, such as an erasableprogrammable read only memory (EPROM) 116, is provided for storing theprogram. One skilled in the art will appreciate that the program couldbe stored on other media, such as on a hard disk or on magnetic tape, inlieu of EPROM 16. The program contains instructions for controlling CPU112 to perform the various routines described above. EPROM 116 has apermanent data base stored therein, which defines the correspondingreference parameters for each truss joint and selected characteristicsof the connector plates to be tested.

CPU 112 communicates with RAM 114 and EPROM 116 via a data bus 118. Toinitialize the program, CPU 112 will address EPROM 116, whereupon theprogram instructions will be executed to control CPU 112. In response tothe program instructions, CPU 112 will establish the boundary vectorscorresponding to the truss profile information entered by the user andwill execute the program steps described above. A standard graphicsprogram may be provided for displaying the truss joint with theconnector plate superimposed thereon on an electronic display, such as acathode ray tube (CRT) display 120. A printer 122 can also be providedfor a hard copy printout.

Various embodiments of the invention have now been described in detail.Since it is obvious that many changes in and additions to theabove-described preferred embodiment may be made without departing fromthe nature, spirit and scope of the invention, the invention is not tobe limited to the details, except as set forth in the appended claims.

What is claimed is:
 1. A method of determining respective lengths ofoverlap of a connector plate on individual wood members of acorresponding truss joint, wherein a Cartesian coordinate system havingan origin corresponding to a predetermined reference point on the jointis established and each wood member is represented by a correspondingtwo-dimensional polygon, each side of which is defined by acorresponding member vector, each of said member vectors having startingand ending points expressed in Cartesian coordinates relative to thereference point, said method comprising the steps of:representing theplate as a corresponding rectangle, each side of which is defined by acorresponding plate vector, each of said plate vectors having startingand ending points expressed in Cartesian coordinates relative to thereference point; selecting a particular one of the wood members anddetermining an area of intersection of the rectangle with the polygondefined by the particular wood member, said area of intersectiondefining an intersection polygon; rotating the intersection polygon andredefining the Cartesian coordinate system of the intersection polygon,so that a first axis thereof is aligned with a central major axisextending along a geometric center of a major surface of a particularwood truss member; measuring maximum and minimum coordinates of theintersection polygon along a second axis of the redefined coordinatesystem, which is perpendicular to the first axis thereof, and adding themaximum and minimum coordinates to determine the length of overlap ofthe connector plate along an axis perpendicular to the central majoraxis of the particular wood member; and repeating the immediatelypreceding three steps with respect to each wood member of the joint todetermine the length of overlap of the plate along an axis perpendicularto the corresponding central major axis of each wood member.
 2. Themethod according to claim 1 further including the steps of determining astress factor in each wood member by computing a magnitude of a forceacting along the central major axis of the corresponding wood member anddividing the magnitude of the force by a product of the length ofoverlap of the connector plate along the second axis and a valuerepresenting thickness of the wood member, as measured along an axisperpendicular to the major surface of the wood member, and comparing thestress factor with a predetermined maximum allowable stress factor todetermine whether the connector plate meets criteria prescribed for thatparticular wood member.
 3. In a data processing system, an apparatus fordetermining respective lengths of overlap of a connector plate onindividual wood members of a corresponding truss joint, wherein aCartesian coordinate system having an origin corresponding to apredetermined reference point on the joint is established and each woodmember is represented by a corresponding two-dimensional polygon, eachside of which is defined by a corresponding member vector, each of saidmember vectors having starting and ending points expressed in Cartesiancoordinates relative to the reference point, said apparatuscomprising:data processing means; input means coupled to said processingmeans for entering selected truss parameters into the system; memorymeans coupled to said processing means for storing said selected trussparameters, said memory means having a predetermined set of programinstructions stored therein; said data processing means being responsiveto said truss parameters for determining respective lengths of overlapof the plate on individual wood members of the truss joint according tosaid program instructions by the following steps:representing the plateas a corresponding rectangle, each side of which is defined by acorresponding plate vector, each of said plate vectors having startingand ending points expressed in Cartesian coordinates relative to thereference point; selecting a particular one of the wood members anddetermining an area of intersection of the rectangle with the polygondefined by the particular wood member, said area of intersectiondefining an intersection polygon; rotating the intersection polygon andredefining the Cartesian coordinate system of the intersection polygon,so that a first axis thereof is aligned with a central major axisextending along a geometric center of a major surface of a particularwood truss member; measuring maximum and minimum coordinates of theintersection polygon along a second axis of the redefined coordinatesystem, which is perpendicular to the first axis thereof, and adding themaximum and minimum coordinates to determine the length of overlap ofthe connector plate along an axis perpendicular to the central majoraxis of the particular wood member; and repeating the immediatelypreceding three steps with respect to each wood member of the joint todetermine the length of overlap of the plate along an axis perpendicularto the corresponding central major axis of each wood member.
 4. Themethod according to claim 3 wherein said data processing means includesmeans for determining a stress factor in each wood member by computing amagnitude of a force acting along the central major axis of thecorresponding wood member and dividing the magnitude of the force by aproduct of the length of overlap of the connector plate along the secondaxis and a value representing thickness of the wood member, as measuredalong an axis perpendicular to the major surface of the wood member, andcomparing the stress factor with a predetermined maximum allowablestress factor to determine whether the connector plate meets criteriaprescribed for that particular wood member.